Pope Francis said Tuesday he wasn't afraid of a U.S. Catholic Church schism led by his conservative critics, but sees a "rigid" ideology opponents use to mask their own moral failings has already infiltrated the American church.

Francis said during an airborne news conference that he prays a schism in the U.S. Catholic Church doesn't happen. He nevertheless doubled down on confronting outspoken conservatives in the U.S. and beyond who oppose his outreach to gay and divorced people and his concern for the poor and the environment.

Francis said he welcomed "loyal" criticism that leads to introspection and dialogue. Such "constructive" criticism shows a love for the church, he said. But he ideologically driven critics don't really want a response but merely to "throw stones and then hide their hand."

"I'm not afraid of schisms," Francis told reporters while the papal plane was flying back from his trip to Africa. "I pray that there aren't any because the spiritual health of so many people is at stake.

"Let there be dialogue, correction if there is some error. But the path of the schismatic is not Christian," he added.

Francis' comments are likely to inflame a heated debate roiling the Catholic Church in the United States and elsewhere. The pope's mercy-over-morals emphasis irks some doctrine-minded Catholics who came of age during the conservative papacies of St. John Paul II and Benedict XVI.

During his flight to Africa last week, a French journalist presented Francis with a book about the pope's conservative critics in the U.S. Francis acknowledged his right-wing opponents and said, "For me, it's an honor if the Americans attack me."

The book, "How America Wants to Change the Pope," documents the growing criticism of Francis by a small wing of U.S. Catholics who question many of his positions. Some have gone so far as to accuse Francis of heresy and warned of the risk of schism, or a formal separation from the Holy See.

Francis' allies, including German Cardinal Walter Kaper and the head of Francis' Jesuit order, have said the conservative criticism amounts to a "plot" to force the first Jesuit pope to resign so a conservative would take his place.

Asked about the criticism and risk of schism, Francis insisted his social teachings were identical to those of St. John Paul II, the standard-bearer for many conservative Catholics.

And he noted that church history is full of schisms, most recently after the Second Vatican Council, the 1960s church meetings that modernized the church.

A group of traditionalist Catholics led by French Archbishop Marcel Lefebvre rejected the reforms and grew into what Francis said was the "most well-known" of recent church schisms.

"I pray there are no schisms, but I'm not afraid of them," he said.

Francis said all schismatics share a common trait: They allow ideology to become "detached" from Catholic doctrine and distance themselves from the faith of ordinary Catholics.

"When doctrine slips into ideology, there's the possibility of schism," he warned.

He lamented that many bishops and priests were already engaged in a "pseudo-schism" but said ideas won't survive.

He claimed doctrinal rigidity, or "moral asceticism," masked their own personal problems. It was perhaps a reference to how some of the church's most notorious sexual predators - the late Legion of Christ leader, Rev. Marciel Maciel among them - preached a highly conservative brand of sexual morals.

"You'll see that behind rigid Christians, bishops and priests there are problems," Francis said, adding that such rigidity showed a lack of a healthy understanding of the Gospel. "We have to be meek with these people who are tempted to attack (because) behind them there are problems and we have to accompany them with meekness."

Opposition to Francis in the U.S. reached a fever pitch in the last year following the publication of accusations by a former Vatican ambassador to the U.S. that Francis, and before him a long list of Vatican and U.S. prelates, turned a blind eye to the sexual misconduct of ex-Cardinal Theodore McCarrick.

Francis didn't name Archbishop Carlo Maria Vigano during his news conference. But he praised critics who spoke to him directly with openness to dialogue.

"At least those who say something have the advantage of honesty in saying so. And I like that," he said. "I don't like criticism when it's under the table, when they smile at you and then then they try to stab you in the back.

"That isn't loyal. That isn't human," Francis said.

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